Too bad Eton is all boys, even in the sixth form. For those of us still eager for the public school experience, the final leaders' debate probably confirmed that, for all its lack of metrosexual trimmings – girls, an abbey, Louis Theroux – an Eton education has the edge over a Westminster one. As for lingering concerns about the more heightened stigma of Eton in the classless world presaged by John Major, Cameron's success confirms that, as Boris Johnson has demonstrated, the Etonian's peculiar whiff of privilege can readily be overlaid by his many other, more significant properties. Unassailable confidence, for instance. Disarming sincerity. Judicious charm. Understated authority. Brazen pisstaking. Just before the last debate, for example, Cameron shyly vouchsafed, to one interviewer, the inspiration for the Big Society he found, as a schoolboy, in a place identified only as "Windsor". Here, he would "visit people", "and do their shopping for them and jobs around the house". Here, perhaps, is a clue to the extraordinary longevity of the royal family: centuries of selfless, Etonian social work.

As things stand, then: Eton two, Westminster one. Had the smooth, Fettesian Blair been competing instead of the socially maladroit Brown, the tournament could have doubled as the first-ever soft-skills It's a Knock Out.

Yet as Brown's nemesis, Mrs Duffy, reminded us, when she heard of her snubbing, he, too, is "an educated man". Even without the private school burnish, Brown's abilities, courtesy of his background and a fast-track through an academic grammar school, gave him advantages that now escape thousands of children, particularly the 40% who leave without five adequate GCSEs. What the prime minister lacks in poise, he makes up for with aggressive intellectual confidence.

In fact, at the same time that they increased to the importance of character in modern elections, the television debates demonstrated the benefits of a classy education in the creation of a character with the required fluency, confidence and self-esteem. If, as some rightly argue, these all-male events have repeatedly exposed the outrageous under-representation of women in public life, they have also advertised the difficulties still to be surmounted by anyone, male or female, from one of Labour's "bog standard" (to use the official term) comprehensives, when forced on to a public stage with a Cameron, Brown or Clegg.

Supposing they can get anywhere near it. Last year, after years of bleating about social mobility, Brown asked Alan Milburn to produce a report on the subject. It concluded that Britain is one of the least socially mobile countries in Europe, largely due to educational inequalities. One in six parents, Milburn said, could not get their children into a decent school. "The problem is not a shortage of parental aspiration. It is a shortage of good schools."

In the three decades since Jim Callaghan feared, in his Ruskin College speech, for the prospects of the poorest children, how much has changed? The Sutton Trust has just affirmed that "children's levels of achievement are more closely linked to their parents' background in England than in many other developed nations". In a new report, "Educational mobility in England", it concludes that, despite "some improvement" during the Labour years, "major inequalities persist". Echoing Milburn, it stressed "high levels of social segregation in English secondary schools" as an obstacle to progress. This coincided with news from Cambridge, that the number of state school pupils admitted dropped by 1% last year. The university's imminent introduction of the A* grade, in order to distinguish between the ever-increasing numbers of children with A grades, there is every chance that this will, again, work against candidates from state schools, particularly those secondaries which do not select, or band, or draw their pupils from middle-class catchments.

Combined with the de-stigmatisation of Cameron (which was partly forced by the privileged educational histories of Labour ministers such as Balls and Harman), and the enhanced visibility of those fine Westminster products, Clegg and Huhne, the extraordinary value of a private education has not been affirmed like this since Tony Blair took over from Wilson, Heath, Callaghan, Thatcher and Major, making him the first independently educated prime minister for 33 years.

Whatever happens this week, it is likely, given the continuing professionalisation of politics, that the overall proportion of privately educated MPs will, in common with the law, medicine and academe, be quite hideous enough to reinforce the choices of parents who have, like me, sought this advantage for their children, and to enrage parents who either despise this option or are otherwise obliged, in the absence of adequate cash, or faith or wangling ability, to educate their children in a borough (like mine) where the secondary schools are shunned even by local Labour politicians. Although, to be fair to my MP, the wealthy Emily Thornberry, I understand she managed to secure some of a handful of places that are reserved for her constituents at an outstanding state secondary situated on the far side of the M25 and is therefore qualified to live the local educational dream: fabulous life chances at no additional cost.

We know by now that a victorious Tory party will contain so many privately educated MPs as to make inevitable the introduction of a uniform, Eton fives and a house system (something the working classes might wish to emulate when they commence setting up their new free schools).

Less predictably, the Guardian has reported that, of 40 Lib Dem candidates for the party's top target seats in this election, just under half went to fee-paying schools, including two Etonians. Tony Travers from the LSE commented: "It is only in Britain that we could have the great revolution led by a group of people who, in background and experience, are more like the existing parties than any other organisation in the country."

But unlike the Labour party, whose dignitaries prefer to gain educational advantage by property transactions or parental piety, Clegg's Lib Dems have, at least, placed social mobility at the top of their manifesto. Their plan is to target funds on struggling pupils and to cut class sizes. While this, presumably because it would upset so many parents, does not begin to address the partial or covert selection that undermines so many state comprehensives, it improves on present neglect, on the Tories' DIY plan, and in many ways Labour's persistent requirement that universities adapt to suit children who have been betrayed by its chaotic secondary education, "widening participation and boosting social mobility".

If only the same duty could have been imposed on the professions, they might have got somewhere. As it is, the debates have foreshadowed the result of Brown's "great moral endeavour", his self-styled "crusade for social mobility": government by patricians. How happy this would have made Harold Macmillan who complained that Mrs Thatcher had more Estonians in her cabinet than Etonians.